Are 3D heat transfer formulations with short time sted and sun

Are 3D heat transfer formulations with short time sted
and sun patch evolution nececessary for building
simulation?
Auline Rodler, Jean-Jacques Roux, Joseph Virgone, E.J. Kim, Jean-Luc
Hubert
To cite this version:
Auline Rodler, Jean-Jacques Roux, Joseph Virgone, E.J. Kim, Jean-Luc Hubert. Are 3D heat
transfer formulations with short time sted and sun patch evolution nececessary for building
simulation?. Building simulation conf´erence 2013, Aug 2013, aix-les-bains, France. pp.37373744. <hal-00985575>
HAL Id: hal-00985575
https://hal.archives-ouvertes.fr/hal-00985575
Submitted on 27 May 2014
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ARE 3D HEAT TRANSFER FORMULATIONS WITH SHORT TIME STEP AND
SUN PATCH EVOLUTION NECESSARY FOR BUILDING SIMULATION?
Rodler A.1, Roux J-J.1, Virgone J.1, Eui-Jong K.1, Hubert J-L.2
1
CETHIL, UMR5008, CNRS, INSA-Lyon, Université Lyon 1, 20 Av A. Einstein,
69621 Villeurbanne Cedex, France
2
Site EDF R&D des Renardières, Avenue des Renardières – Ecuelles, 77818 Moret-sur-Loing
Cedex, France
ABSTRACT
A numerical model is developed to accurately
simulate the transient thermal behaviour of rooms
with sun-facing windows, with the use of a refined
spatial and temporal discretization. For each node,
the energy balance equations are developed based on
a consideration of radiation, convection, air enthalpy
and three-dimensional heat conduction. As buildings
are exposed to rapid climatic variations (particularly
incident solar radiation), we have added the different
environmental conditions at short time-steps. The
simulation considers the projection of solar radiation
through a window onto interior walls, referred to as a
sun patch. Therefore conduction transfer is treated in
three dimensions. The indoor air temperature, the
temperature of the cells in the walls and the surface
temperatures are calculated at each time step using a
variable-step Ordinary Differential Equation (ODE)
solver.
Results from this model are compared to well-known
simulation tools using one-dimensional heat
conduction without a sun patch.
of heat conduction through a wall in one dimension
only. Another drawback of TnrSys when performing
short time step simulations of thick and highly
insulated walls is its reliance on the Conduction
Transfer Function method. Such problems have
previously been reported by other authors (FloryCelini, 2008; Delcroix et al., 2011; Savoyat et al.,
2011).
As a thermal model of a building envelope should
take into account rapid environmental variations, we
have decided to develop a new transient thermal
model that provides a faithful description heat
transfer through walls in 3D over a short timescale.
This numerical three dimensional transient thermal
model is introduced in the following section of this
paper. In order to evaluate the importance of the
novel features and the critical parameters of the
model (control volume size, sampling rate, and sun
patch simulation), the model was systematically
compared to contemporary models under a range of
simulation configurations.
INTRODUCTION
MODEL DEVELOPMENT
In France, the residential sector represents 42 % of
energy consumption (ADEME, 2005). The French
building code is guiding the construction sector to
embrace low energy building practices. This
regulation imposes limitations on maximal primary
energy consumption, the use of the energy systems,
and upper limits on air infiltration. In order to comply
with these standards, low-energy buildings may
incorporate high levels of insulation, heat recovery
systems and passive solar building design techniques.
The building envelope is modeled following a three
dimensional approach. The model represents a single
room with a large window. The thermal behavior to
be included in the model is summarized as follows:
As low energy buildings are generally well insulated,
overheating of rooms can be a serious issue.
Therefore, it is important to assess the performance
of current transient thermal models when adapted to
low energy buildings, defined as those with
particularly thick and insulated walls. Contemporary
thermal models, like TrnSys (TRNSYS Mathematical
Reference, 1996), Dymola (Dymola Version 2013)
and Codyba (www.jnlog.com/codyba1.htm) are
typically used to predict performance over the course
of a year. As a result, certain features of heat transfer
in building envelopes are simplified or neglected, for
instance the location of a sun patch, or the treatment
– Solar radiation exchange (short-wave and long
wave) with the sun patch and the radiation
distribution
– Three-dimensional heat conduction
– Enthalpy of a single air node
– Convection between wall surfaces, the external and
internal environment.
The walls of the model are simulated as a finite
element mesh. Optimization of the meshing through
the wall and its surfaces is described in a following
section. Note that the model considers a single air
node.
For each control volume, its temperature ܶ is given
by the partial differential heat conduction equation in
three dimensions, coupled to the sum of convective
and radiative exchange ʣ୘୓୘ :
‫ܸܥ‬
డ்
డ௧
డ்
ൌ ߣ௫ ቀ ቁ
డ்
ߣ௫ ቀ ቁ
డ௫ ௫ି೏ೣ
డ்
ߣ௬ ቀ ቁ
మ
డ௫ ௫ା೏ೣ
డ௬ ௬ି೏೤
మ
డ்
ߣ௭ ቀ ቁ
where
డ௭ ௭ି೏೥
మ
మ
݀‫ ݖ݀ݕ‬െ
డ்
݀‫ ݖ݀ݕ‬൅ ߣ௬ ቀ ቁ
డ௬ ௬ା೏೤
మ
డ்
݀‫ ݖ݀ݔ‬൅ ߣ௭ ቀ ቁ
డ௭ ௭ା೏೥
݀‫ ݕ݀ݔ‬൅ ʣ୘୓୘ మ
݀‫ ݖ݀ݔ‬െ
ι
‫ܧ‬ௌௐǡ௜
=߬ௗ ‫ܩ‬ௗ ܴௗ if the element i is not
included in the sun patch
(1)
݀‫ ݕ݀ݔ‬െ
ʣ୘୓୘ ൌ ʣୗ୛ ൅ ʣ୐୛ ൅ ʣେ୓୒୚
(2)
and ʣେ୓୒୚ is the convective heat flow between the
surface and its environment and ʣ୐୛ and ʣୗ୛ are
the long wave and short wave radiation. Thermal
conductivities in the three directions are designated
ߣ௫ =ߣ௬ =ߣ௭ [W/mK] and the volumetric heat capacity
is denoted by ‫[ ׋‬J/m3K].
The energy balance equation for the air in the room
with temperature ܶ௔௜ is:
ே
߲ܶܽ݅
ߩ‫׋‬௔௜௥ ܸ௖
ൌ ෍ ܳ‫׋‬௔௜௥ ሺܶ௔௘ െ ܶ௔௜ ሻ
߲‫ݐ‬
௡ୀ଴
ேெ
(3)
൅ ෍ ݄ܵ௖௜ ሺܶௌூ െ ܶ௔௜ ሻ
௝ୀଵ
Here ܶ௔௘ is the exterior dry bulb temperature (°C), ܳ
is the air flow (kg/s),‫׋‬௔௜௥ the heat capacity of the air
(J/kgK), ߩthe air density (kg/m3), ܸ௖ the volume of
the room, ܶௌூ the interior surface temperature and ݄௖௜
the convective transfer coefficient. ܰ‫ ܯ‬is the number
of radiation balance equations corresponding to the
number of surface mesh elements and ܰ the number
of zones (here ܰ =1).
Short wave radiation
The total short wave radiation absorbed by the
surfaces of a control volume is given by the vector
the vector:
ሼʣୗ୛୍ ሽ ൌ ሾܵሿሾܽௌௐூ ሿሼ‫ܧ‬ௌௐ ሽ
(4)
where ሾܵሿ is the surfaces matrix and ሾܽௌௐூ ሿ is the
matrix of absorptivities of the control volumes of the
internal wall for the short wave radiation. ሼ‫ܧ‬ௌௐ ሽ is
the vector of radiation received by the mesh
elements, obtained by resolving:
ι ሽ
൅ ሾܵሿሾߩሿሾ‫ܨܨ‬ሿሼ‫ܧ‬ௌௐ }
ሾܵሿሼ‫ܧ‬ௌௐ ሽ ൌ ሾܵሿሼ‫ܧ‬ௌௐ
(5)
Where ሾߩሿ is the reflectivity matrix. The view factors
of the matrix ሾ‫ܨܨ‬ሿ are calculated following the
ι
Nusselt analog (unit hemisphere). ሼ‫ܧ‬ௌௐ
ሽ is the vector
composed by primary radiation received by the
control volumes. It results from the horizontal beam
radiation ‫ܩ‬௕ and the diffuse radiation ‫ܩ‬ௗ received by
the mesh elements:
ι
‫ܧ‬ௌௐǡ௜
= ߬௕ ‫ܩ‬௕ ܴ௕ +߬ௗ ‫ܩ‬ௗ ܴௗ , if the element i is
in the sun patch, and
(6)
߬௕ and ߬ௗ are the direct and diffuse transmission
coefficients of the glass and depend on the incidence
angle of the beam, whereas Rbൌ ܿ‫ݏ݋‬ሺߠሻȀܿ‫ݏ݋‬ሺߠ‫ݖ‬ሻ
and Rdൌ ሺͳ ൅ ܿ‫ݏ݋‬ሺ‫݌‬ሻሻȀʹ provide direct and diffuse
radiation components on a titled surface with slope ‫݌‬
(Esveev and Kudish, 2008)( Liu et al., 1969).
The sun patch position has been calculated by a
geometrical test: the boundary of the window is
projected on an orthogonal plane to the beam. The
control volumes of the walls are projected on the
same plane, and thus those projected cells belonging
to the projection of the window are identified.
The short wave radiation received by the control
volumes of external walls are determined depending
on the position of the walls relative to the sun
according to:
ሼʣୗ୛୉ ሽ ൌ ሾܵሿሾܽௌௐா ሿሼ‫ܩ‬௕ ܴ௕ ൅ ‫ܩ‬ௗ ܴௗ ൅
ሺ‫ܩ‬ௗ ൅ ‫ܩ‬௕ ሻܴ௥ ሽ
(7)
With Rr ൌ ሺͳ െ ܿ‫ݏ݋‬ሺ‫݌‬ሻሻ݈ܾܽȀʹ, and alb the ground
albedo, which is the outside reflectivity of the
ground.
Long wave radiation
Long wave radiation of the control volumes or the
cells in the room of temperatures ሼܶௌூ ሽare given by:
ሼʣ୐୛୍ ሽ ൌ ሾܽ௅ௐூ ሿሾܵሿߪሼܶௌூ ସ െ ܶ௠ସ ሽ
(8)
which is linearized to:
ሼʣ୐୛୍ ሽ
ିଵ
ൌ ሾߝሿሾܵሿ ൤ሾ‫ܫ‬ሿൣሾ‫ܫ‬ሿ െ ሾ‫ܨܨ‬ሿሾߩሿ൧ ሾ‫ܨܨ‬ሿሾߝሿ൨ ‫ܴܪ‬ሼܶௌூ
െ ܶ௠ ሽ
(9)
where ሾ‫ܫ‬ሿ is the unit matrix, ሾ‫ܨܨ‬ሿ the view factor
matrix and ሾߝሿ emissivity matrix of the cells in the
wall. The radiation coefficients ‫ ܴܪ‬were fixed to 5.8
W/m²K.
Radiative heat transfer between external walls and
the sky with effective temperatureܶ௦௞௬ , and with the
ground with temperatureܶ௘௔௥௧௛ is given by:
ሼʣ୐୛୉ ሽ ͳ ൅ ܿ‫݌ ݏ݋‬
൰ ൫ሼܶ௦௞௬ ሽ െ ሼܶௌா ሽ൯
ʹ
ͳ െ ܿ‫݌ ݏ݋‬
൅ ݄௥௘ ሾܵሿ ൬
൰ ሺሼܶ௘௔௥௧௛ ሽ െ ሼܶௌா ሽሻ
ʹ
ൌ ݄௥௦ ሾܵሿ ൬
(10)
where ݄௥௦ ൌ ݄௥௘ are the radiative coefficients with
the ground and the sky. These were also fixed to 5.8
W/m²K.
Convective heat transfer
Convective heat flows between the environment and
the external surface of the walls are given by:
ʣ஼ைே௏ ൌ ݄௖௘ ሾሿሼܶܽ݁ െ ܶௌா ሽ
(11)
where ݄௖௘ ൌ ʹͳ W/m²K is the external convective
coefficient.
The convective heat flux with the internal
environment is:
ʣ஼ைே௏ ൌ ݄௖௜ ሾሿሼܶܽ݅ െ ܶௌூ ሽ
(12)
where the internal convective coefficient was
assumed to be ݄௖௜ ൌ ͺ W/m²K
General resolution of the model
The input data are the building characteristics and the
meteorological measurements. The numerical mesh
of the room is generated with HEAT3 in cartesian
coordinates (Blomberg, 1996).
Differential equations 1 and 2 are solved with a
function of Matlab (ode23t). This function solves
moderately stiff ordinary differential equations using
the trapezoidal rule or Runge Kutta. This method is
interesting because it solves the equations with an
adapted and variable time-step. For fluctuant input
data this method would automatically shorten the
time step; similarly it would expand the time for
periods with little fluctuation.
simulations were performed for a time-varying sun
patch.
First model: simplified hypotheses
For the first simulation the simplest case of one cell
per surface was considered, neglecting reflections
inside the room.
A visualization of this simple model, seen from the
outside, is shown below generated in HEAT3 (Figure
1).
SIMULATIONS AND DISCUSSIONS
The absorptivity and emissivity coefficients of the
window and walls are listed in the table below.
Table 1: absorptivity and reflexivity of the wall and
window
ܽௌௐூ of the wall
ܽௌௐூ of the window
ܽௌௐா of the wall
ܽௌௐா of the window
ܽ௅ௐா
Ε
1
0.05
0.6
0.05
0.9
0.9
Figure 1: Shape and mesh of the room in HEAT3, the
window appears in white
Each wall is described by only two cells. However,
their connection to adjacent cells ensures that the
heat transfer by conduction remains three
dimensional.
For the same set of minute-wise weather data, the air
temperature ܶܽ݅ predicted by the model was
compared to that obtained to Dymola (Dymola
Version
2013)
and
TRNSYS
(TRNSYS
Mathematical Reference, 1996) in order to verify
consistency for this simplified arrangement (Figure
2).
25
20
Tai (°C)
For all the simulations the same room dimensions
were used: 3.01 m in width, 3.16 m in depth and
3.36 m in height. The walls, the ceiling and the roof
are made of 10 cm thick concrete (ߣ=2.7 W/mK) and
the room has a 1 cm thick window located on the
south-facing wall (ߣ=1 W/mK)). Air flow in the
room was neglected for all the simulations.
Convective and radiative transfer coefficients are
kept constant throughout the simulations.
15
10
Minute-wise weather data were used from the
meteorological station of Vaulx-en-Velin, France
(latitude: 45°46’43’’N and longitude : 4°55’21’’E,
height 170m) (http://idmp.entpe.fr/vaulx/mesfr.htm).
As a proof of principle test, the first model comprised
the simple case of one control volume per internal
surface and all radiation projected on the ground.
Figure 2: Comparison between TRNSYS - Dymola –
our model
The model was subsequently transformed to more
detailed configurations. As a first step, the
importance of the weather data sampling was
assessed. Then, the influence of cell size was
analyzed and optimized for this room. Finally,
The small discrepancies observed may arise from
slightly different calculations of short and long wave,
the one dimensional approach employed by TRNSYS
and Dymola, and the solver algorithms. Differences
between 0 and 1°C degrees are observed between our
5
0
1 Apr
2 Apr
Our Model
3 apr
TrnSys
4 Apr
Dymola
First model: sampling
Once we checked the general coherence of the
model, we were interested in the sampling of weather
data and its impact on the building simulation.
Weather data are often taken at the time step of one
hour. This time step may be sufficiently accurate if
the aim is to study the overall behavior of a building
during a year. It is poorly adapted however, to
transient simulations designed to study the detailed
thermal behavior of the envelope. To overcome this,
Escudero (1989) modeled the perturbations as
mathematical functions and applied Shannon’s
sampling theorem. He concluded that to represent
outside bulb temperature variation in time a 40 min
time step is enough, and a 5 and 2 min time step are
enough for the diffuse and direct radiation.
For the first more detailed simulation, we chose to
keep the radiation data at the time step of one minute,
in order to keep the short-time solar variations. So,
the model needs to solve the differential equations
(1) and (2) for each sample of weather data. For the
second simulation, a set of hourly data was generated
by integrating minute-wise data in the previous hour.
Simulation results using these aggregated data are
shown superposed over those obtained with minutewise measured weather data in Figure 3. The same
number of cells was used for the two simulations. In
red, we can see simulations using one minute time
step measured weather data as an input of the model
and in green, results with hourly input data.
Minute-wise data were retained for the following
tests and simulations, in order to reveal any effects of
these fluctuations on the numerical model. Note that
this time step was not optimized. Indeed, a two or
even three minute time step could be adequate.
First model: study of the spatial discretization
The importance of the cell size was first studied
through the wall thickness. For a model, the greater
the nodal discretization of the system, the finer the
the calculated dynamics. Note that the time step of
the thermal model and the narrowness of the spatial
discretization of the described thermal system are
interrelated.
When significant variations occur, for example
fluctuations in solar radiation, the parts of the walls
closest to the surfaces are the most affected.
Considering the perturbations studied, the mesh
resolution was enhanced in the edge regions in order
to provide more detailed information near the surface
next to these gains. So, it seems obvious to refine the
cells next to the surfaces in contact with the room’s
volume. Figure 4 shows the interior air temperature
of the room for 2,4,8 and 13 cells and with a fine
meshing near the surface.
25
20
Tai (°C)
results and Dymola and differences between 0 and
2°C are observed between TrnSys and our model.
15
10
5
1200
25
0
01 Apr
8 Cells
15
10
400
ai
800
T (°C)
G (W/m²)
20
5
0
4 Apr
Global radiation
0
1 mn time step weather data
1 h time step weather data
Figure 3: Impact of hourly and minute time-step
weather data on the air temperature simulation
Short term variations in total radiation are clearly
visible on the blue curve also shown in the figure.
The weather fluctuations have an impact on the
results simulated with the model for weather data
with a time-step of one minute. Hourly data tend to
smooth the fluctuations of the solar radiation and this
has an impact on the building simulation results.
Differences up to 1°C were observed on the air
temperature calculation of the cell for the data
sample.
02 Apr
13 Cells
03 Apr
4 Cells
04 Apr
2 Cells
Figure 4: Air temperature for different spatial
discretization
With few control volumes, fluctuations in air
temperature are smooth. As the control volumes are
thicker, the first volumes near the room absorb more
of the solar variations by conduction.
The temperature differences, in green, vary from 0 to
2.3°C between a model with two and eight cells
(Figure 5). These differences are largest when total
incident solar radiation fluctuations are greatest.
Indeed, we observe fewer differences for the third
day, a day with less direct incident solar radiation.
For this wall thickness and with 13 cells, we observe
very little difference with the model with eight cells.
In conclusion, 8 cells seem adequate and will be kept
in the wall for the following tests as it seems enough
to absorb the perturbations. More cells would cause
longer calculation times.
Differences (°C)
2
800
1
400
0
01 Apr
02 Apr
03 Apr
04 Apr
Global irradiation (W/m²)
1200
0
Figure 5: In black global incident solar radiation
and in green the air temperature differences
For the same hypotheses, we compared the previous
result (with a finer mesh through the thickness of the
wall) and a simulation with a finer discretization of
the wall surfaces (Figure 6). The red scattered line is
the air temperature variation in time for one cell per
surface but eight cells perpendicular to the wall.
25
ai
T (°C)
20
15
10
5
0
4 Apr
144 cells per wall
One cell per wall
Figure 6: Influence of the spatial discretization of the
walls’ surfaces
In the figure, the blue line shows the results for a
discretization of 144 cells per wall side and eight
cells perpendicular to the wall. For this case, the
three dimensional approach of the model has a
greater influence on heat transfer. Thermal
capacitance is more important as well as we observe
that the response of air temperature to fluctuations in
solar incident solar radiation. The air temperature
differences between the two simulations are between
0 and 1.69 °C for the 4th April.
Second model: sun patch integration
Some of the gains which until now have been
neglected are becoming more important in transient
thermal modelling in low energy buildings
(Duforestel et al., 2008). It is the case of fast
variation of incident solar radiation and their
distribution or what we call sun patch.
However Wall (1997) shows that it is important to
consider the sun patch distribution, especially for
heating requirements of glazed spaces.
Tittelein (2008) determines the sun position and
projects the sun patch on the walls. He assigns to
each wall a percentage of short wave radiation that
varies in time. He shows that there is a difference of
8.5% for heating requirements between a model
considering the sun patch and one without it. The
next step now is to know whether assigning to each
wall the same percentage of incident solar radiation
is accurate enough. Indeed, a uniform distribution of
solar heat flux on the walls seems adapted to one
dimensional heat conduction; if we want to calculate
accurately the impact of the perturbations it is
important to locate the sun patch and therefore
meshing the surfaces of the walls is necessary.
In order to locate the sun patch, the walls have been
meshed in all the directions. In each direction we
have 28 cells, 8 in each the wall’s thickness and 12
on the surfaces. Internal reflections are integrated
thanks to the view factors and absorptivity of the
walls was fixed to 0.6 and reflexivity to 0.4. Finally,
a three dimensional approach would be the best to do
if we want to couple the sun patch movement and a
transient thermal model. A better localization of the
sun patch enables to locate overheating and the
creation of plumes. These temperature differences
will modify mean radiant temperature which is a
comfort criterion.
The position of the sun patch depends on the position
of the sun and the orientation of the building. On the
figure below we show three moments in the day
(morning, midday and afternoon) with the sun patch
location (Figure 7 and 8). We have represented the
cells located in the inside of the room. In black, no
sun patch touches the cells of the walls, in gray it is
the window and in white we show the cells touched
by the sun patch. Note that the gray cells represent
the window and it is oriented south.
Figure 7: Sun patch location for the 4th April: morning
and midday
The incoming incident solar radiation in a room is
projected as a sun patch. In most of the modeling
approaches, the incoming incident solar radiation is
constantly projected on the floor. Other hypotheses
are to project only 60% of the incident solar radiation
on the floor.
Figure 8: Sun patch location in the afternoon
Cross section of the eastern wall
We can see that for a simulation in April, the sun
patch touches partially the floor, the wall oriented
east and the one oriented west.
Number of meshes in the y direction
22
th
At 14h48 UTC on the 4 April, we have the inside
temperature distribution shown on Figure 9.At this
moment of the day, the sun patch is mainly on the
floor and on the wall oriented east.The sun patch is
clearly located, because the cells receiving important
short wave radiation reach 22°C. Reflections are
observed on the adjacent cells. Temperature
differences between one cell and another cell can
reach 8.8°C. Besides, the impact of the solar sun
patch inside the room has an important effect on heat
conduction transfer inside the walls.For the same
simulated day and time we looked at the crosssection of two walls by fixing a height (Figure 10).
At this moment the air of the cell is at 18.54°C and
the outside temperature is of 13.4°C. We can observe
that the cells of the first figure (Figure 10), which are
never in the sun patch, are quite homogenous in
temperature. On the second figure we can see that at
the left hand side we have high temperatures, which
are located in the sun patch. There is clearly a
temperature gradient, and the magnitude of the
gradient rises towards the sun patch.
T(°C)
11
21
20
9
19
7
18
17
5
16
TA
3
15
14
1
1
3
5
7
Number of meshes in the x direction
Figure 10: Horizontal cross-section of the cells and
their temperature (height = 0.35cm)
This 3D heat transfer model compared to a simpler
model is more discretized and a cell can be touched
during a certain time by the sun patch, but at another
moment it will be receiving only reflections or only
diffuse radiation coming from other surfaces. We
studied the temperature variation in time of cell TA
and TB shown on figure 11. The red dotted line
represents the temperatures of the cell TA and the
unbroken blue line is the temperature of the cell TB.
Cell TB is never receiving direct solar radiation
during this day but in the morning it will be hotter
than the cell TA as it is located nearer to the sun
patch at this moment. In the afternoon, when the sun
patch is located on the opposite side, cell TA is
warmer. Temperature differences for these two cells
during one day are between 0 and 4.6°C. The room’s
air temperature (black scattered line) depends on all
the surrounding cells’ temperatures and therefore is
located in between of the other curves.
25
Cross section of the northern wall
T (°C)
15
10
5
22
15
Number of meshes in the y direction
T (°C)
20
Figure 9: Inside temperature distribution of the floor,
window and the wall oriented east at 14h48 UTC
0
4 Apr
21
13
TA
20
11
19
9
TB
Tai
Figure 11: Temperature of cell TA and TB and the
temperature of the room’s air
18
7
17
5
16
3
1
15
TB
1
3
5
7
9
11
Number of meshes in the x direction
14
The heating of some areas of the wall due to the sun
patch changes the transferred conduction fluxes to
the outside. This is observed on the external surfaces
where higher temperatures are observed where the
nearby meshed volumes were touched by the sun
patch (Figure 12) located on the inside of the eastern
wall (Figure 9).
CONCLUSION
Figure 12: Outside temperature distribution of the
floor, window and the wall oriented east at 14h48
UTC on the 4th April
We have compared the results from the first study
done with a constant projection of the short wave
radiation on the floor to this study with the sun patch
model. In blue, we can see the room’s air temperature
when we project all the incident solar radiation on the
floor with the same absorptivity and reflectivity than
for the sun patch model. The black dotted line is the
air temperature variation in time after integrating the
sun patch. When integrating the sun patch we have
the same incoming radiation through the window
than with no sun patch, but the spatial distribution of
the radiation touching the walls and control volumes
are different. With the sun patch we have fewer cells
touched by the direct radiation than when projecting
the radiation on the floor. Therefore with the sun
patch model, we tend to have higher temperatures for
the cells touched by the sun patch but we have a
smaller area than when supposing that the radiation
touches the whole floor’s surface. In average, with
the sun patch model we have temperature differences
between the surfaces and the air which are smaller
than with the other model. That is the reason why,
the air temperature ܶ௔௜ has a smaller gradient when
we add the sun patch (Figure 13). Over all, we obtain
a less fluctuant temperature variation with the sun
patch integration, than with the simple case.
Differences between 0 – 1.09°C are observed.
25
Tai (°C)
FUTURE WORK
These results have to be validated with experimental
data, and therefore we are working on an in situ
experimental set up.
ACKNOLEDGEMENTS
This work has been supported by the French National
Agency for Research (ANR), in the framework of the
project "SUPERBAT", ANR-10-HABISOL-004-06.
I would also like to thank Leon Gaillard and Pierrick
Haurant for their contributions.
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0
We have started with a simplified model and with
current taken hypotheses: few cells, all the short
wave radiation on the floor and hourly weather data.
We have gradually transformed this model in a more
complex model, by working on the sampling rate, the
spatial discretization and the sun patch simulation.
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the sun patch leads to important improvements,
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4 Apr
W ithout sun patch
W ith sun patch
Figure 13: Air temperature of the cell for two
simulations: with and without sun patch
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